1. Finite-State Machines with Output

2. Example of a FSM with Output
A vending machine accepts nickels (5¢), dimes (10¢), and quarters (25¢). When 30¢ or more has been deposited, the machine returns the amount over 30¢. The customer can then press an O-button to receive orange juice or an R-button to receive apple juice

3. Example of a FSM with Output
The same FSM can be represented using a table

4. FSMs with Outputs
A finite-state machine M = (S, I, O, f, g, s0) consists of:
a finite set S of states
a finite input alphabet I
a finite output alphabet O
an initial state s0
a transition function f
an output function g
Example 1:
S = {s0, s1, s2, s3}
I = {0, 1}
O = {0, 1}
Initial: s0
f, g: state table/diagram

5. FSMs with Outputs Example 2: unit-delay machine
given the bit string x1x2…xk it produces 0x1x2…xk-1

6. FSMs with Outputs Example 3: adding machine for binary integers
given (xn…x1x0)2 and (yn…y1y0)2 it produces their sum